Calculation of Magnetoelectric Brushless DC Electric Motor in Polar Coordinates

The electromagnetic calculation of magnetoelectric switched-type motors with high-energy permanent magnets by the method of separating Fourier variables in polar coordinates is considered. A two-dimensional analytical model is used taking into account the real geometry of permanent magnets, stator slots with a fixed finite magnetic permeability of the teeth and the yoke of the stator and rotor cores. To do this, the single magnetic field of the machine is divided into a set of cylindrical strips, analyzed independently of each other. At the boundaries of the strips, the conditions for conjugating magnetic fields are met: scalar magnetic potentials and normal components of magnetic induction do not undergo jumps. Magnetic potentials are determined from the solution of the Dirichlet boundary value problem, and induction, which is usually determined from the solution of the Neumann boundary value problem, is here determined by differentiating the expression for the magnetic potentials.. The latter eliminates the need to solve additionally the Neumann boundary value problem. In this case, an original technology for finding Fourier constants is used, based on the equality of magnetic potentials and magnetic inductions at the boundaries of the strips. Graphs of magnetic induction in the air gap at the pole division are presented, obtained taking into account the stator gearing, winding harmonics of the magnetomotive force and the geometric structure of the arrangement of permanent magnets. It has been shown that bevel of the stator slots by a tooth pitch makes it possible to eliminate the reactive torque of the motor.